Numerical Simulation of Reactive Flow

Oran, Elaine S.; Boris, J. P.

doi:10.1017/cbo9780511574474

Cited by 476 publications

(472 citation statements)

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“…Following the work [16,17], ARK N methods can be used to solve the equations of the form: [5] that adopted in this work are third-order, fourth-order, and fifth-order ARK2 methods, respectively. Meanwhile, the non-stiff convective term in this paper was numerically discretized in space using fifth-order WENO scheme [22][23][24][25][26][27][28][29].…”

Section: Methodsmentioning

confidence: 99%

“…The practical implicit methods for gaseous detonation simulation can be categorized into two classes, i.e. the time-splitting method and the additive semi-implicit method [2,3].The time-splitting methods [4][5][6][7][8], resolve the source term of reactive Euler equations into ( ) ( ),   t …”

mentioning

confidence: 99%

“…The time-splitting methods [4][5][6][7][8], resolve the source term of reactive Euler equations into ( ) ( ),   t…”

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confidence: 99%

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Additive Runge-Kutta methods for H2/O2/Ar detonation with a detailed elementary chemical reaction model

Ren

Ning

2013

Chin. Sci. Bull.

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We report here the additive Runge-Kutta methods for computing reactive Euler equations with a stiff source term, and in particular, their applications in gaseous detonation simulations. The source term in gaseous detonation is stiff due to the presence of wide range of time scales during thermal-chemical non-equilibrium reactive processes and some of these time scales are much smaller than that of hydrodynamic flow. The high order, L-stable, additive Runge-Kutta methods proposed in this paper resolved the stiff source term into the stiff part and non-stiff part, in which the stiff part was solved implicitly while the non-stiff part was handled explicitly. The proposed method was successfully applied to simulating the gaseous detonation in a stoichiometric H 2 /O 2 /Ar mixture based on a detailed elementary chemical reaction model comprised of 9 species and 19 elementary reactions. The results showed that the stiffly accurate additive Runge-Kutta methods can capture the discontinuity well, and describe the detonation complex wave configurations accurately such as the triple wave structure and cellular pattern. Reacting flows, specifically in gaseous combustion, have been a significant topic of active research for more than one hundred years. The strong coupling between hydrodynamic flow and chemical kinetics is complex and even today many phenomena are not very well understood yet. Gaseous detonation is a process of supersonic combustion in which a shock wave is propagated and supported by the energy release in a reaction zone behind it. It is the more powerful and destructive of the two general classes of combustion, the other one being deflagration. The primary difficulty in computing reacting flows is the source term stiffness inherent in the reactive Euler equations in temporal integrations. Besides, the viscous stress and heat flux terms in the boundary layers can cause the stiffness too. The source terms are stiff because the thermal-chemical non-equilibrium reactive processes possess a wide range of time scales and some of them are much smaller than that of hydrodynamic flow [1]. The simulation will be inefficient when the explicit methods rather than the implicit methods are used, because the time-step sizes dictated by the stability restraint in explicit methods are much smaller than those required by the CFL condition. Due to these limitations in explicit methods, the implicit methods are normally required to simulate gaseous detonation. The practical implicit methods for gaseous detonation simulation can be categorized into two classes, i.e. the time-splitting method and the additive semi-implicit method [2,3].The time-splitting methods [4][5][6][7][8], resolve the source term of reactive Euler equations into ( ) ( ),   t

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Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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Additive Runge-Kutta methods for H2/O2/Ar detonation with a detailed elementary chemical reaction model

Ren

Ning

2013

Chin. Sci. Bull.

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“…[13] In order to solve the transport equations, the fluxcorrected-transport technique of Boris and Book [1976] is employed with time step splitting being used to solve the equations in three dimensions [Oran and Boris, 2001].…”

Section: Numerical Techniquementioning

confidence: 99%

Global neutral polar wind model

Gardner

Schunk

2005

J. Geophys. Res.

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[1] The neutral polar wind shows a highly dynamic structure that depends on the characteristics of convection and precipitation. The ions in the polar wind are highly dependent on convection electric fields at high latitudes, and their outflow dynamics are modified by the heat input of precipitating electrons in the auroral zone. A new three-dimensional model of the neutral polar wind has been developed which takes into account the convecting ion polar wind and heating due to precipitating electrons in the auroral zone, along with charge exchange between the ion polar wind and the background thermal and geocoronal neutral atoms. The results show that over the polar caps the neutral polar wind particles exhibit extremely large fluxes in both the horizontal and vertical directions, and to a fixed observer it would appear that the neutral polar wind particles are moving in all directions. The results also show that the heating that occurs during geomagnetic storms leads to a significant coupling between the ionosphere and magnetosphere via both ion and neutral particles.

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“…Representative examples include reaction networks in combustion chemistry [1], geochemical cycling of elements [2], and thermonuclear reaction networks in astrophysics [3,4]. The differential equations used to model these networks usually exhibit stiffness, which arises from multiple timescales in the problem that differ by many orders of magnitude [1,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Algebraic stabilization of explicit numerical integration for extremely stiff reaction networks

Guidry

2012

Journal of Computational Physics

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In contrast to the prevailing view in the literature, it is shown that even extremely stiff sets of ordinary differential equations may be solved efficiently by explicit methods if limiting algebraic solutions are used to stabilize the numerical integration. The stabilizing algebra differs essentially for systems well-removed from equilibrium and those near equilibrium. Explicit asymptotic and quasi-steady-state methods that are appropriate when the system is only weakly equilibrated are examined first. These methods are then extended to the case of close approach to equilibrium through a new implementation of partial equilibrium approximations. Using stringent tests with astrophysical thermonuclear networks, evidence is provided that these methods can deal with the stiffest networks, even in the approach to equilibrium, with accuracy and integration timestepping comparable to that of implicit methods. Because explicit methods can execute a timestep faster and scale more favorably with network size than implicit algorithms, our results suggest that algebraically-stabilized explicit methods might enable integration of larger reaction networks coupled to fluid dynamics than has been feasible previously for a variety of disciplines.

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Numerical Simulation of Reactive Flow

Cited by 476 publications

References 2 publications

Additive Runge-Kutta methods for H2/O2/Ar detonation with a detailed elementary chemical reaction model

Additive Runge-Kutta methods for H2/O2/Ar detonation with a detailed elementary chemical reaction model

Global neutral polar wind model

Algebraic stabilization of explicit numerical integration for extremely stiff reaction networks

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